Let 0 = - be the measure of the angle between the vectors u and 0.If ||T'|| = 6 and ||D'|| = 4, then compute CA) || 3 7- 2 u|| (B) ||u + 3 7'|| (C) ū • (T + 2 v) (D) (U + 3 v') •(2 u-7)

Q: (a) Let u and v be two vectors in R³ such that |u|| = 3 and ||v|| = 9. (i) Find the maximum and…

A:

Q: 3 Among all unit vectors u = y in R', find the one for which the sum x + 8y+ 4z is minimal.

A:

Q: ors are parallel u= and U= None of the others \(\) 6 \(\) -3 \(1) 2 10) 3

A:

Q: Suppose f(x,y) = = tan(x) + y and u is the unit vector in the direction of (-3,-1). Then, a) ▼ f(x,…

A:

Q: Q2) Find T N „B of the vectors the curve r(t) = at the point (1, ,1)

A:

Q: If AT = ul v. A and if the vectors U and V satisfy Au 5u and Av = 7v, then True False

A:

Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

A:

Q: Let S = {(0,1,0), (,0, ), (, 0, )}. The %3D set S is an orthonomal set of vectors. If u = (2, 2, 1),…

A: see below the answer  here we use the system of equation to find (u)S

Q: The velocity of an object is given by V(t) = ti + e'j + te'k. Find the position function of the…

A:

Q: Find the vectors T, N, and B at the given point. T = N = = B = r(t) = (4 cos(t), 4 sin(t), 4…

A: Answer

Q: Let h(x, y) = x² + 3xy - 6y. In what direction does h increase most rapidly at the point (3, 2)? (a)…

A:

Q: ū = (-/3, –1) and w = (1, /3) E. |

A:

Q: Find the vector equation for the line of intersection of the planes x + y - 4z = 4 and + 4z = -2

A: We have to find the vector equation.

Q: 123. If F is a vector point function and a is a constant vector then show that i) V (a · F) = (a-V)…

A:

Q: (a) Consider two vectors u = 3 and v = 5 in R4, Show that 5 7 7 i) u.v = v.u ii) d(u, v) > 0 [-31

A: Two vectors u and v is given in R4, and the vector is given as:

Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

A:

Q: Given the vector-valued function r (t) = e-t i +t j +(tan t) k Find: a) r'(t) b) r"(t) c) r'(t) .…

A:

Q: Please justify whether these statements are true of false. a. If u and v are vectors in R^3, then…

A: Objects with both magnitude and direction are called vectors. The vector's size is determined by the…

Q: et u and v be vectors in R 3 such that ∥u∥ = 30 and ∥v∥ = 5. What can we best say about |u · v|? (a)…

A: One must verify a few claims, using the rule of dot product.

Q: Q1. If the components of a contravariant vector in (x') coordinate system are (3,4). Find its…

A: 1) Given information: x¯1 = 7x1 - 5x2x¯2 = -5x1 + 4x2 The components of contravariant in xi…

Q: Let A and B be vectors in R" and let c be a real number. Then (1) ||A|| 2 0, and || A|| = 0 if and…

A:

Q: Let x' = (1, 1, 3) and y' = (-2, 0, -2). calculate the angle between x and y

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.